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A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers

Author

Listed:
  • József Dombi

    (HUN-REN SZTE, Research Group on Artificial Intelligence, 6701 Szeged, Hungary
    Institute of Informatics, University of Szeged, 6701 Szeged, Hungary
    These authors contributed equally to this work.)

  • Jenő Fáró

    (Faculty of Economics, Eötvös Loránd University, 1053 Budapest, Hungary
    These authors contributed equally to this work.)

  • Tamás Jónás

    (Faculty of Economics, Eötvös Loránd University, 1053 Budapest, Hungary
    These authors contributed equally to this work.)

Abstract

In group decision making, the knowledge, skills, and experience of the decision-makers may not be at the same level. Hence, the need arises to take into account not only the opinion, but also the relative importance of the opinion of each decision-maker. These relative importance values can be treated as weights. In a group decision making situation, it is not only the weighted aggregate output that matters, but also the weighted measure of the group consensus. Noting that weighted group consensus measures have not yet been intensely studied, in this study, based on well-known requirements for non-weighted consensus measures, we define six reasonable requirements for the weighted case. Then, we propose a function family and prove that it satisfies the above requirements for a weighted consensus measure. Hence, the proposed measure can be used in group decision making situations where the decision-makers have various weight values that reflect the relative importance of their opinions. The proposed weighted consensus measure is based on the fuzziness degree of the decumulative distribution function of the input scores, taking into account the weights. Hence, it may be viewed as a weighted adaptation of the so-called fuzziness measure-based consensus measure. The novel weighted consensus measure is determined by a fuzzy entropy function; i.e., this function may be regarded as a generator of the consensus measure. This property of the proposed weighted consensus measure family makes it very versatile and flexible. The nice properties of the proposed weighted consensus measure family are demonstrated by means of concrete numerical examples.

Suggested Citation

  • József Dombi & Jenő Fáró & Tamás Jónás, 2025. "A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers," Mathematics, MDPI, vol. 13(3), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:526-:d:1584235
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    References listed on IDEAS

    as
    1. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.
    2. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
    3. József Dombi & Jenő Fáró & Tamás Jónás, 2023. "A Fuzzy Entropy-Based Group Consensus Measure for Financial Investments," Mathematics, MDPI, vol. 12(1), pages 1-18, December.
    4. Dombi, József & Jónás, Tamás, 2022. "Weighted aggregation systems and an expectation level-based weighting and scoring procedure," European Journal of Operational Research, Elsevier, vol. 299(2), pages 580-588.
    5. Yan, Hong-Bin & Ma, Tieju & Huynh, Van-Nam, 2017. "On qualitative multi-attribute group decision making and its consensus measure: A probability based perspective," Omega, Elsevier, vol. 70(C), pages 94-117.
    6. J. C. R. Alcantud & R. Andrés Calle & J. M. Cascón, 2015. "Pairwise Dichotomous Cohesiveness Measures," Group Decision and Negotiation, Springer, vol. 24(5), pages 833-854, September.
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    8. Dombi, József & Jónás, Tamás, 2024. "Consensus measures based on a fuzzy concept," European Journal of Operational Research, Elsevier, vol. 315(2), pages 642-653.
    9. Chiclana, F. & Herrera-Viedma, E. & Herrera, F. & Alonso, S., 2007. "Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 182(1), pages 383-399, October.
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